Gelfand-Levitan-Krein method in one-dimensional elasticity inverse problem
2021 ◽
Vol 2092
(1)
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pp. 012022
Keyword(s):
The One
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Abstract In this article we propose the numerical solution of the one dimensional inverse coefficient problem for seismic equation. We use a dynamical version of Gelfand-Levitan-Krein approach for reducing a nonlinear inverse problem for recovering the shear wave’s velocity and the density of the medium to two sequences of the linear integral equations. We propose numerical algorithm for solving these equations based on a fast inversion of a Toeplitz matrix. The proposed numerical methods base on the structure of the problem and therefore improve the efficiency of the algorithms, compared with standard approaches. We present numerical results for solving considered integral equations.
2015 ◽
Vol 23
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2016 ◽
Vol 52
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pp. 1142-1149
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1977 ◽
Vol 11
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pp. 729-740
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2006 ◽
Vol 52
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pp. 933-940
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2005 ◽
Vol 160
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pp. 579-587
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2019 ◽
Vol 38
(4)
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